Two-dimensional materials are of current great interest for their promising applications to postsilicon microelectronics. Here we study, using first-principles calculations and a Monte Carlo simulation, the electronic structure and magnetism of CrI3 monolayer, whose bulk material is an interesting layered ferromagnetic (FM) semiconductor. Our results show that CrI3 monolayer remains FM with , and the FM order is due to a superexchange in the near-90° Cr-I-Cr bonds. Moreover, we find that an itinerant magnetism could be introduced by carriers doping. Both electron doping and hole doping would render CrI3 monolayer half-metallic, and steadily enhance the FM stability. In particular, hole doping is three times as fast as electron doping in increasing TC, and a room temperature FM half-metallicity could be achieved in CrI3 monolayer via a half-hole doping. Therefore, CrI3 monolayer would be an appealing two-dimensional spintronic material.